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A formula is an algebraic relationship between two or more variable
quantities.
For example, A = lw is a formula for the area, A,
of a rectangle of length l and width w. In the
formula, A is expressed in terms of l and w. We
say that A is the subject of the formula.
If we know the values of l and w, the corresponding value
of A is determined by substituting l and w into the
formula. However, if we know the values of A and l and
are required to find the value of w, then it is convenient to
rearrange the formula in order to express w in terms of A
and l as follows:
Now w is the subject of the formula.
The process of expressing w in terms of A and l is
called transposition or changing the subject
of the formula. The methods used to change the subject of the
formula are the same as those used for solving
equations.
Literal Equations
The methods used to transpose literal equations are the same as those
for solving equations.
Transpositions Involving One Operation
To rearrange the terms in a formula, the same operations are performed
to both sides of the formula, i.e. whatever is done to one side of the
formula must be done to the other.
Transpositions Involving Addition
Recall that:
The same number can be added to each side of a formula.
Example 34
Solution:
Key Terms
formula, subject of a formula,
transposition, changing the subject,
literal equation
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